Partially Balanced Incomplete Block Designs

Abstract

Bose and Nair (1939) introduced a class of binary, equireplicate and proper designs, which are called Partially Balanced Incomplete Block (PBIB) designs. In these designs the variance of every estimated elementary contrast among treatment effects is not the same. PBIB designs are classified into different types on the basis of their association schemes. In brief, they can be grouped as PBIB(2) designs, PBIB(3) designs and higher associate-class PBIB designs. In each of these groups there are further sub groups based on the type of the underlying association scheme. Here in this seminar group divisible, triangular, rectangular, nested group divisible, right angular and circular (4) association schemes and the PBIB designs based on these schemes are described.